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posted by  Chase725 on 11/4/2009 12:58:58 AM  |  status: Live  |  Earned Karma: 25

Help Please, Thanks. Tangental Speed

Course Textbook Chapter Problem Needs by
General Physics Physics (7th) by Cutnell, Johnson N/A N/A 11/4/2009 at 5:00:00 AM
Question Details:
Interactive LearningWare 8.2 provides a view of the concepts that are important in this problem. A race car, starting from rest, travels around a circular turn of radius 28.3 m. At a certain instant, the car is still accelerating, and its angular speed is 0.421 rad/s. At this time, the total acceleration (centripetal plus tangential) makes an angle of 37.3° with respect to the radius. (The situation is similar to that in Figure 8.13 b in the text, reproduced below.) What is the magnitude of the total acceleration?

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Section 8.4 Angular Variables and Tangential Variables

Section 8.5 Centripetal Acceleration and Tangential Acceleration

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posted by jerry2009 on 11/5/2009 2:19:24 AM  |  status: Live
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Response Details:


    Radius, R = 28.3 m

    Angular speed, ω = 0.421 rad / s

    Angle made by resultant acceleration ( a )  with Centripetal acceleration ( ac ) , φ = 37.3 o

    Centripetal acceleration, ac = ω2 R
                                             = 0.421 2 * 28.3
                                             = 5.02 m / s2

    tan φ = aT / ac    ( where aT = tangential acceleration )

    aT = ac  tan φ
        = 5.02 * 0.7618
        = 3.824 m / s2

    Total acceleration, a = [ ( ac ) 2 + ( aT ) 2 ] 1/2

                                   = ( 5.02 2 + 3.824 2 ) 1/2

                                              = 6.31 m / s2
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